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THEORETICAL AND COMPUTATIONAL PLASMA PHYSICS 156 9 Theoretical and Computational Plasma Physics INTRODUCTION AND BACKGROUND Plasma physics is the study of collective processes in many-body charged- particle systems. Like the fields of condensed matter physics and molecular biology, plasma physics is founded on well-known principles at the microscopic level. In the case of plasma physics, the description is based on the Liouville equation or kinetic equations for the electron and ion distribution functions in a multidimensional phase space and Maxwell's equations, whose sources are self- consistent moments of the distribution functions. The plasma state is distinguished by the existence of a vast number of collective motions over a very wide range of spatial and temporal scales. The interaction of these collective motions often leads to turbulence or coherent patterns and structures. Indeed, coherent patterns frequently may coexist with turbulence. A priori theoretical prediction of plasma behavior has enjoyed only limited success. Therefore, experiments are critical to the identification of fundamental processes in a plasma, such as the evolution of coherent structures arising from nonlinear interactions. These, in turn, form the intellectual building blocks for understanding the evolution of yet more complex processes. The history of plasma science is as diverse as the subject itself. In Chapter 8 above, early work in laboratory plasma science is described, beginning with the work of Faraday in the 1830s on the chemical transformation of the elements and continuing with Langmuir's work on gas discharges in the 1920s and research on electron beams and beam-type microwave devices in the 1940s and 1950s. Within a decade of Langmuir's work, the discovery that radio waves reflect from
THEORETICAL AND COMPUTATIONAL PLASMA PHYSICS 157 the ionosphere established the existence of the space plasma that surrounds the Earth. A new era in plasma physics began with the international development of efforts to achieve controlled thermonuclear fusion in the 1950s and with the space program, which began with the launching of Sputnik in 1957. For the past 30 years, space, fusion, and the development of advanced weapons systems have been the main drivers for plasma science. Early in the space and fusion programs, a rich variety of fundamental configurations and phenomena were investigated, but as a rule, nonlinear processesâalthough fascinating scientificallyâproved to be a detriment to the achievement of fusion plasma conditions in the laboratory. As a consequence, fusion research evolved to focus on systems with the least complexity consistent with programmatic goals. Inertial fusion research evolved in directions that either minimized nonlinear laser-plasma interactions or optimized particle-beam drivers. Magnetic fusion research concentrated on the tokamak approach, the most stable axisymmetric confinement configuration. The principal difficulty encountered in fusion and in defense applications has been the inability to predict the nonlinear behavior of plasmas to an accuracy required by engineering considerations. A successful example of such a prediction is illustrated in Figure 9.1. In the exploration of space plasmas, it was not possible to reduce the natural complexity of the magnetic field geometry through engineering design. Spacecraft data have identified many key nonlinear phenomena: collisionless shocks, bursty and steady magnetic reconnection, double layers, current sheets, dynamo generation of magnetic fields, and the overall structure of magnetospheric plasmas, which are high-mirror-ratio magnetic confinement configurations. Up until now, because spacecraft obtain local data, only the rudimentary aspects of these processes have been measured. While the discoveries of plasma phenomena in the space environment are remarkably varied, their abstractions into basic plasma processes subject to investigation by computational simulation, laboratory experiments, and analytical theory have lagged because support, especially for laboratory experimentation, has ''practically vanished" in the words of the Brinkman report, Physics Through the 1990s.1 Notable exceptions exist, of course, and these are presented later in this chapter. The next decade could promise a fundamental reversal of this paradigm, provided the resources for basic plasma experimentation described in Chapter 8 become available. One can anticipate that plasma phenomena discovered through spacecraft and astronomical observations, as well as fusion research, will play an important role in motivating laboratory experimentation. Moreover, the theo 1 National Research Council, Plasmas and Fluids, in the series PhysicsThrough the 1990s, National Academy Press, Washington, D.C., 1986.
THEORETICAL AND COMPUTATIONAL PLASMA PHYSICS 158 FIGURE 9.1 Theoretical model of the "fishbone" oscillations observed in tokamak plasmas. This figure shows that the high-frequency modulation of the magnetic field occurs in bursts (lower trace); it also shows the induced loss of high-energy particles during each burst, by the decrease in the normalized pressure of the energetic particles, Î² h. (Reprinted, by permission, from L. Chen, R.B. White, and M.N. Rosenbluth, Physical Review Letters 52:1122, 1984. Copyright Â© 1984 by the American Physical Society.)